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Assuming that there are X machines in this batch, it is expected to be completed in x/4 days.

4*3/2=6 (unit)

That is, after improving efficiency, six machines can be installed every day.

According to the meaning of the question: (2/3 * x)/4+(1/3 * x)/6 = (1/4 * x)-1.

That is, the time to install 2/3 machines under the original efficiency plus the time to install 1/3 machines after improving efficiency is one day less than originally expected.

Solution: x=32, x/4=8.

A: This batch of 32 machines is expected to be completed in 8 days.